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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="lambda.extending"></a>Extending return type deduction system</h2></div></div></div>
<p>


In this section, we explain  how to extend the return type deduction system 
to cover user defined operators. 

In many cases this is not necessary, 
as the BLL defines default return types for operators.

For example, the default return type for all comparison operators is 
<code class="literal">bool</code>, and as long as the user defined comparison operators 
have a bool return type, there is no need to write new specializations 
for the return type deduction classes.

Sometimes this cannot be avoided, though.

</p>
<p>
The overloadable user defined operators are either unary or binary. 

For each arity, there are two traits templates that define the 
return types of the different operators.

Hence, the return type system can be extended by providing more 
specializations for these templates.

The templates for unary functors are

<code class="literal">
plain_return_type_1&lt;Action, A&gt;
</code>

and 

<code class="literal">
return_type_1&lt;Action, A&gt;
</code>, and 

<code class="literal">
plain_return_type_2&lt;Action, A, B&gt;
</code>

and 

<code class="literal">
return_type_2&lt;Action, A, B&gt;
</code>

respectively for binary functors.

</p>
<p>
The first parameter (<code class="literal">Action</code>) to all these templates 
is the <span class="emphasis"><em>action</em></span> class, which specifies the operator. 

Operators with similar return type rules are grouped together into 
<span class="emphasis"><em>action groups</em></span>, 
and only the action class and action group together define the operator 
unambiguously. 

As an example, the action type 
<code class="literal">arithmetic_action&lt;plus_action&gt;</code> stands for 
<code class="literal">operator+</code>. 

The complete listing of different action types is shown in 
<a class="xref" href="extending.html#table:actions" title="Table 20.2. Action types">Table 20.2, “Action types”</a>. 
</p>
<p>
The latter parameters, <code class="literal">A</code> in the unary case, 
or <code class="literal">A</code> and <code class="literal">B</code> in the binary case, 
stand for the argument types of the operator call. 

The two sets of templates, 
<code class="literal">plain_return_type_<em class="parameter"><code>n</code></em></code> and 
<code class="literal">return_type_<em class="parameter"><code>n</code></em></code> 
(<em class="parameter"><code>n</code></em> is 1 or 2) differ in the way how parameter types 
are presented to them.

For the former templates, the parameter types are always provided as 
non-reference types, and do not have const or volatile qualifiers.

This makes specializing easy, as commonly one specialization for each 
user defined operator, or operator group, is enough.

On the other hand, if a particular operator is overloaded for different 
cv-qualifications of the same argument types, 
and the return types of these overloaded versions differ, a more fine-grained control is needed.

Hence, for the latter templates, the parameter types preserve the 
cv-qualifiers, and are non-reference types as well. 
 
The downside is, that for an overloaded set of operators of the 
kind described above, one may end up needing up to 
16 <code class="literal">return_type_2</code> specializations.
</p>
<p>
Suppose the user has overloaded the following operators for some user defined 
types <code class="literal">X</code>, <code class="literal">Y</code> and <code class="literal">Z</code>:

</p>
<pre class="programlisting">
Z operator+(const X&amp;, const Y&amp;);
Z operator-(const X&amp;, const Y&amp;);
</pre>
<p>

Now, one can add a specialization stating, that if the left hand argument 
is of type <code class="literal">X</code>, and the right hand one of type 
<code class="literal">Y</code>, the return type of all such binary arithmetic 
operators is <code class="literal">Z</code>:

</p>
<pre class="programlisting">
namespace boost { 
namespace lambda {
  
template&lt;class Act&gt; 
struct plain_return_type_2&lt;arithmetic_action&lt;Act&gt;, X, Y&gt; {
  typedef Z type;
};

}
}
</pre>
<p>

Having this specialization defined, BLL is capable of correctly 
deducing the return type of the above two operators.

Note, that the specializations must be in the same namespace, 
<code class="literal">::boost::lambda</code>, with the primary template. 

For brevity, we do not show the namespace definitions in the examples below.
</p>
<p>
It is possible to specialize on the level of an individual operator as well, 
in addition to providing a specialization for a group of operators. 
Say, we add a new arithmetic operator for argument types <code class="literal">X</code> 
and <code class="literal">Y</code>:

</p>
<pre class="programlisting">
X operator*(const X&amp;, const Y&amp;);
</pre>
<p>

Our first rule for all arithmetic operators specifies that the return 
type of this operator is <code class="literal">Z</code>, 
which obviously is not the case.
Hence, we provide a new rule for the multiplication operator:

</p>
<pre class="programlisting">
template&lt;&gt; 
struct plain_return_type_2&lt;arithmetic_action&lt;multiply_action&gt;, X, Y&gt; {
  typedef X type;
};
</pre>
<p>
</p>
<p>
The specializations can define arbitrary mappings from the argument types 
to the return type. 

Suppose we have some mathematical vector type, templated on the element type:

</p>
<pre class="programlisting">
template &lt;class T&gt; class my_vector;
</pre>
<p>

Suppose the addition operator is defined between any two 
<code class="literal">my_vector</code> instantiations, 
as long as the addition operator is defined between their element types. 

Furthermore, the element type of the resulting <code class="literal">my_vector</code> 
is the same as the result type of the addition between the element types.

E.g., adding <code class="literal">my_vector&lt;int&gt;</code> and 
<code class="literal">my_vector&lt;double&gt;</code> results in 
<code class="literal">my_vector&lt;double&gt;</code>.

The BLL has traits classes to perform the implicit built-in and standard 
type conversions between integral, floating point, and complex classes.

Using BLL tools, the addition operator described above can be defined as:

</p>
<pre class="programlisting">
template&lt;class A, class B&gt; 
my_vector&lt;typename return_type_2&lt;arithmetic_action&lt;plus_action&gt;, A, B&gt;::type&gt;
operator+(const my_vector&lt;A&gt;&amp; a, const my_vector&lt;B&gt;&amp; b)
{
  typedef typename 
    return_type_2&lt;arithmetic_action&lt;plus_action&gt;, A, B&gt;::type res_type;
  return my_vector&lt;res_type&gt;();
}
</pre>
<p>
</p>
<p>
To allow BLL to deduce the type of <code class="literal">my_vector</code> 
additions correctly, we can define:

</p>
<pre class="programlisting">
template&lt;class A, class B&gt; 
class plain_return_type_2&lt;arithmetic_action&lt;plus_action&gt;, 
                           my_vector&lt;A&gt;, my_vector&lt;B&gt; &gt; {
  typedef typename 
    return_type_2&lt;arithmetic_action&lt;plus_action&gt;, A, B&gt;::type res_type;
public:
  typedef my_vector&lt;res_type&gt; type;
};
</pre>
<p>
Note, that we are reusing the existing specializations for the 
BLL <code class="literal">return_type_2</code> template, 
which require that the argument types are references. 
</p>
<div class="table">
<a name="table:actions"></a><p class="title"><b>Table 20.2. Action types</b></p>
<div class="table-contents"><table class="table" summary="Action types">
<colgroup>
<col>
<col>
</colgroup>
<tbody>
<tr>
<td><code class="literal">+</code></td>
<td><code class="literal">arithmetic_action&lt;plus_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">-</code></td>
<td><code class="literal">arithmetic_action&lt;minus_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">*</code></td>
<td><code class="literal">arithmetic_action&lt;multiply_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">/</code></td>
<td><code class="literal">arithmetic_action&lt;divide_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">%</code></td>
<td><code class="literal">arithmetic_action&lt;remainder_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">+</code></td>
<td><code class="literal">unary_arithmetic_action&lt;plus_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">-</code></td>
<td><code class="literal">unary_arithmetic_action&lt;minus_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&amp;</code></td>
<td><code class="literal">bitwise_action&lt;and_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">|</code></td>
<td><code class="literal">bitwise_action&lt;or_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">~</code></td>
<td><code class="literal">bitwise_action&lt;not_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">^</code></td>
<td><code class="literal">bitwise_action&lt;xor_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&lt;&lt;</code></td>
<td><code class="literal">bitwise_action&lt;leftshift_action_no_stream&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&gt;&gt;</code></td>
<td><code class="literal">bitwise_action&lt;rightshift_action_no_stream&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&amp;&amp;</code></td>
<td><code class="literal">logical_action&lt;and_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">||</code></td>
<td><code class="literal">logical_action&lt;or_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">!</code></td>
<td><code class="literal">logical_action&lt;not_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&lt;</code></td>
<td><code class="literal">relational_action&lt;less_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&gt;</code></td>
<td><code class="literal">relational_action&lt;greater_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&lt;=</code></td>
<td><code class="literal">relational_action&lt;lessorequal_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&gt;=</code></td>
<td><code class="literal">relational_action&lt;greaterorequal_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">==</code></td>
<td><code class="literal">relational_action&lt;equal_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">!=</code></td>
<td><code class="literal">relational_action&lt;notequal_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">+=</code></td>
<td><code class="literal">arithmetic_assignment_action&lt;plus_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">-=</code></td>
<td><code class="literal">arithmetic_assignment_action&lt;minus_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">*=</code></td>
<td><code class="literal">arithmetic_assignment_action&lt;multiply_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">/=</code></td>
<td><code class="literal">arithmetic_assignment_action&lt;divide_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">%=</code></td>
<td><code class="literal">arithmetic_assignment_action&lt;remainder_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&amp;=</code></td>
<td><code class="literal">bitwise_assignment_action&lt;and_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">=|</code></td>
<td><code class="literal">bitwise_assignment_action&lt;or_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">^=</code></td>
<td><code class="literal">bitwise_assignment_action&lt;xor_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&lt;&lt;=</code></td>
<td><code class="literal">bitwise_assignment_action&lt;leftshift_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&gt;&gt;=</code></td>
<td><code class="literal">bitwise_assignment_action&lt;rightshift_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">++</code></td>
<td><code class="literal">pre_increment_decrement_action&lt;increment_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">--</code></td>
<td><code class="literal">pre_increment_decrement_action&lt;decrement_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">++</code></td>
<td><code class="literal">post_increment_decrement_action&lt;increment_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">--</code></td>
<td><code class="literal">post_increment_decrement_action&lt;decrement_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">&amp;</code></td>
<td><code class="literal">other_action&lt;address_of_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">*</code></td>
<td><code class="literal">other_action&lt;contents_of_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">,</code></td>
<td><code class="literal">other_action&lt;comma_action&gt;</code></td>
</tr>
<tr>
<td><code class="literal">-&gt;*</code></td>
<td><code class="literal">other_action&lt;member_pointer_action&gt;</code></td>
</tr>
</tbody>
</table></div>
</div>
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